Matrix Algebra Explained

In this course, you will learn about the basics of matrices in algebra. While this is not a linear algebra course, it will serve to get you up to speed with most of the entry level topics taught in a linear algebra course. In this course, you will learn the following:

• How to Solve Linear Systems Using Gaussian Elimination

• How to Solve Linear Systems Using Gauss-Jordan Elimination

• How to Place an Augmented Matrix in Row Echelon Form

• How to Place an Augmented Matrix in Reduced Row Echelon Form

• How to Add Matrices

• How to Subtract Matrices

• How to Multiply a Matrix by a Scalar

• How to Multiply Matrices

• How to Find the Inverse of a Matrix using Row Reduction

• How to Solve Linear Systems using Matrix Equations (Using the Inverse of a Matrix)

• How to Find the Determinant of a Matrix Using Laplace Expansion

• How to Find the Determinant of a 3 x 3 Matrix Using the Shortcut

• How to Find the Determinant of a Matrix in Upper Triangular Form 4 x 4 Shortcut

• How to Find the Transpose of a Matrix

• How to Find the Classical Adjoint (Adjugate of a Matrix)

• How to Find the Inverse of a Matrix Using the Determinant and the Adjoint (Adjugate)

• How to Solve a 2 x 2 Linear System Using Cramer's Rule

• How to Solve a 3 x 3 Linear System Using Cramer's Rule

• Applications of Determinants - Finding the Area of a Triangle

• Applications of Determinants - Testing for Collinearity

• Applications of Determinants - Finding the Equation of a Line Using Determinants